minimize the sum of c_j / x_j subject to the sum of x_j <= 1000000
1000000 variables in [0.01, 10], c_j = 1 + (j mod 9), from x_j = 0.5
iteration  best value        largest error of a variable
        0  9.9999920000e6                         6.4e-1
        4  9.9999920000e6                          1.9e0
        8  9.9999920000e6                         9.8e-1
       12  4.8556119309e6                         3.7e-1
       16  4.6146391143e6                         1.6e-1
       20  4.6016040237e6                         1.0e-2
       24  4.6014970171e6                         6.5e-6
       28  4.6014970170e6                         6.6e-9
       31  4.6014970170e6                        9.5e-10
converged by the step after 31 iterations and 32 evaluations
value 4.6014970170e6, the minimum 4.6014970170e6
largest relative error of a variable 2.7e-9, the volume used 999999.999997 (violation 0.0e0)
multiplier 4.6014970177, the exact (sum of the roots of c_j)^2 / V^2 = 4.6014970170
